Degenerate parabolic partial differential equations (PDEs) with vanishing or unbounded leading coefficient make the PDE non-uniformly parabolic, and new theories need to be developed in the context of practical applications of such rather unstudied mathematical models arising in porous media, population dynamics, financial mathematics, etc. With this new challenge in mind, this paper considers investigating newly formulated direct and inverse problems associated with non-uniform parabolic PDEs where the leading space- and time-dependent coefficient is allowed to vanish on a non-empty, but zero measure, kernel set. In the context of inverse analysis, we consider the linear but ill-posed identification of a space-dependent source from a time-integral observation of the weighted main dependent variable. For both, this inverse source problem as well as its corresponding direct formulation, we rigorously investigate the question of well-posedness. We also give examples of inverse problems for which sufficient conditions guaranteeing the unique solvability are fulfilled, and present the results of numerical simulations. It is hoped that the analysis initiated in this study will open up new avenues for research in the field of direct and inverse problems for degenerate parabolic equations with applications.
Mercifulness is a trait of civilization, humanity, and a moral value in society, because it has an impact on social life and its role in spreading interdependence, joint liability, and solidarity among people. Mercifulness means spreading mercy, synergy, sympathy, and cooperation. Generally, a society that enjoys strong ties tends to have a kind of stability and development, as well as, is able to face the economic, political, and security crises. Conversely, a weak society leads to weak social cohesion and weak community infrastructure that is more vulnerable to social, economic, and political instability. Thus, this is the aim of the research that has used a social survey method applied to a sample of respondents who have reached (300)
... Show MoreE-Learning packages are content and instructional methods delivered on a computer
(whether on the Internet, or an intranet), and designed to build knowledge and skills related to
individual or organizational goals. This definition addresses: The what: Training delivered
in digital form. The how: By content and instructional methods, to help learn the content.
The why: Improve organizational performance by building job-relevant knowledge and
skills in workers.
This paper has been designed and implemented a learning package for Prolog Programming
Language. This is done by using Visual Basic.Net programming language 2010 in
conjunction with the Microsoft Office Access 2007. Also this package introduces several
fac
Physiological status and litter size can indeed have a significant impact on ewes' hematological parameters, which are essential indicators of their health. Therefore, this study examined the hematological profiles of ewes during pregnancy with single and twins in the Awassi ewes. The present study involved 232 ewes in good health and at sexual maturity. Among them, 123 ewes had single pregnancies, while 109 ewes had twin pregnancies. The age range of the ewes included in the study was between 3.5 and 4.5 years. Hematological tests were conducted on the sheep's blood samples promptly following collection. The findings demonstrated variations in hematological parameters among pregnant
... Show MoreObjective: To determine the quality assurance for maternal and child health care services in Baghdad City.
Methodology: A descriptive study is conducted throughout the period of November 28th 2008 to October 10th
2009. A simple random sample of (349) is selected through the use of probability sampling approach. The study
sample was divided into four groups which include (220) consumers, (35) medical staff, (72) nursing staff and (22)
organization structure (primary health care centers). Data were collected through the use of assessment tools. It was
comprised of four questionnaires and overall items included in these questionnaires are (116) items. The study
included assessment of organization structure. Data were colle
Many approaches of different complexity already exist to edge detection in
color images. Nevertheless, the question remains of how different are the results
when employing computational costly techniques instead of simple ones. This
paper presents a comparative study on two approaches to color edge detection to
reduce noise in image. The approaches are based on the Sobel operator and the
Laplace operator. Furthermore, an efficient algorithm for implementing the two
operators is presented. The operators have been applied to real images. The results
are presented in this paper. It is shown that the quality of the results increases by
using second derivative operator (Laplace operator). And noise reduced in a good
Simple, cheap, sensitive, and accurate kinetic- spectrophotometric method has been developed for the determination of naringenin in pure and supplements formulations. The method is based on the formation of Prussian blue. The product dye exhibits a maximum absorbance at 707 nm. The calibration graph of naringenin was linear over the range 0.3 to 10 µg ml-1 for the fixed time method (at 15 min) with a correlation coefficient (r) and percentage linearity (r2%) were of 0.9995 and 99.90 %, respectively, while the limit of detection LOD was 0.041 µg ml-1. The method was successfully applied for the determination of naringenin in supplements with satisfac
... Show MoreB3LYP density functional is utilized for probing the effect of decorating Al, Ga, and In on the sensing performance of a boron phosphide nanotube (BPNT) in detecting the 2-chloroethanol (CHE) molecule. We predict that the interaction of pure BPNT with CHE is physisorption, and the sensing response (SR) of BPNT is approximately 6.3. The adsorption energy of CHE is about − 26.3 to − 91.1, − 96.6, and − 100.3 kJ/mol, when the Al, Ga, and In metals are decorated on the BPNT surface, respectively. This indicates that the decorated metals significantly strength the interaction. Also, the corresponding SR meaningfully rises to 19.4, 41.0, and 93.4, indicating that by increasing the atomic number of metals, the sensitivity i
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